It seems that for my car, Audi A3 Sportback [8V] (2013 onwards), there is no suitable rear carrier available!
This maybe due to the Sportback fitting made out of plastic or fibreglass. I have been looking at Halford, Saris and the Roofbox website with the same results, not suitable. And I don't have a towbar.
Anyway, maybe I should hold off for the moment, as it's a company car and due for renewal next year (if I'm lucky). We are allowed to specify extras so I might just go for the towbar if it's another similar model. I don't take the bike by car that often, it's probably preferable (and cheaper) to faff around with putting it inside the car, for the time being.